Question: Ben is 4 times as old as Michael. Eight years ago, Ben was 6 times as old as Michael. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Michael. Let Ben's current age be $b$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $b = 4m$ Eight years ago, Ben was $b - 8$ years old, and Michael was $m - 8$ years old. The information in the second sentence can be expressed in the following equation: $b - 8 = 6(m - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = b / 4$ . Substituting this into our second equation, we get: $b - 8 = 6($ $(b / 4)$ $- 8)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 8 = \dfrac{3}{2} b - 48$ Solving for $b$ , we get: $\dfrac{1}{2} b = 40$ $b = 2 \cdot 40 = 80$.